The Fokker–Planck equation for coupled Brown–Néel-rotation
The Fokker–Planck equation for coupled Brown–Néel-rotation
复制标题
耦合布朗-尼尔旋转的福克-普朗克方程
DOI：
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发表时间：
2018
影响因子：
3.5
通讯作者：
J. Weizenecker
中科院分区：
文献类型：
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作者：
J. Weizenecker
计算单畴粒子磁化强度的动态特性对于磁粒子成像（MPI）具有重要意义。虽然在施加随时间变化的磁场后的瞬时热力学平衡（朗之万函数）的假设足以理解基本行为，但必须考虑磁性粒子的有限响应时间，以优化或分析各个方面，例如解释光谱，优化MPI序列，开发新的对比度和评估简化模型。磁场作用后磁化强度的变化是由两种不同的运动引起的：粒子的几何旋转和磁化强度相对于固定粒子轴的旋转。这些单独的旋转可以很好地用朗之万方程或福克-普朗克方程来描述。然而，由于两个旋转通常表现出相互依赖性，因此有必要考虑两个方程之间的耦合。本文介绍了如何在耦合朗之万方程的基础上导出耦合福克-普朗克方程。导出了两个物理等价的Fokker-Planck方程，并通过适当的级数展开将其转化为一个常微分方程组，从而可以数值求解。最后，这个系统也被用来指定各种极限情况下的微分方程系统（Néel，Brown，单轴对称）。一般来说，该系统表现出稀疏填充矩阵，因此可以很好地处理数字。
Calculating the dynamic properties of magnetization of single-domain particles is of great importance for the tomographic imaging modality known as magnetic particle imaging (MPI). Although the assumption of instantaneous thermodynamic equilibrium (Langevin function) after application of time-dependent magnetic fields is sufficient for understanding the fundamental behavior, it is essential to consider the finite response times of magnetic particles for optimizing or analyzing various aspects, e.g. interpreting spectra, optimizing MPI sequences, developing new contrasts, and evaluating simplified models. The change in magnetization following the application of the fields is caused by two different movements: the geometric rotation of the particle and the rotation of magnetization with respect to the fixed particle axes. These individual rotations can be well described using the Langevin equations or the Fokker–Planck equation. However, because the two rotations generally exhibit interdependence, it is necessary to consider coupling between the two equations. This article shows how a coupled Fokker–Planck equation can be derived on the basis of coupled Langevin equations. Two physically equivalent Fokker–Planck equations are derived and transformed by means of an appropriate series expansion into a system of ordinary differential equations, which can be solved numerically. Finally, this system is also used to specify a system of differential equations for various limiting cases (Néel, Brown, uniaxial symmetry). Generally, the system exhibits a sparsely populated matrix and can therefore be handled well numerically.
影响因子：
3.8
作者：
Ferguson, R. Matthew;Minard, Kevin R.;Krishnan, Kannan M.
通讯作者：
Krishnan, Kannan M.
影响因子：
3.2
作者：
Reeves, Daniel B.;Weaver, John B.
通讯作者：
Weaver, John B.